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inverse of a polynomial modulo another polynomial

asked 2012-02-28 11:47:08 +0200

anonymous user


updated 2012-02-28 12:07:01 +0200

DSM gravatar image

Hi, I'm trying to implement the Baby Step Giant Step algorithm in the group of units of prime fields. I would like to generate the field provided one generator polynomial. But I need to calculate p^(-1) (where p is a polynomial), but can't find a function to do so. This is what I'm doing,

F.<a> = GF(2)[];
R.<b> = PolynomialRing(F)
S.<x> = R.quotient(b^4+b+1)

m = sqrt(S.modulus().degree()); 
gamma = S.modulus();
alpha = x^3+1;

now i need to calculate (alpha)^(-1) modulo gamma

Any help? Better ways to do the same thing?


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You should look up the extended gcd algorithm. This is implemented by the xgcd() function in Sage.

burcin gravatar imageburcin ( 2012-02-28 12:56:29 +0200 )edit

Burcin, xgcd doesn't work. It fails with a type error, "cannot coerce nonconstant polynomial".

Simon King gravatar imageSimon King ( 2012-02-28 18:11:20 +0200 )edit

If you define R over the fraction field of F, or simply over GF(2), then alpha^-1 yields the answer.

Francis Clarke gravatar imageFrancis Clarke ( 2012-02-29 03:27:44 +0200 )edit

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answered 2017-03-05 20:18:12 +0200

dan_fulea gravatar image
sage: F.<b> = GF(2)[]
sage: S.<x> = GF( 2**4, modulus = b^4 + b + 1 )
sage: 1/(x^3+1)
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Asked: 2012-02-28 11:47:08 +0200

Seen: 4,802 times

Last updated: Mar 05 '17